Question

Write an exponential equation in the form y = abx whose graph passes through points (4, 8) and (6, 32).

y = 4(8)x


y = 2(0.5)x


y = 0.5(2)x


y = (0.5)x

Answer 1

Option C.

Explanation:

The general exponential equation is

`y=ab^x`

It is given that the graph of exponential function passes through points (4,8) and (6,32). It means the equation of exponential function must be satisfied by these points.

`8=ab^4` ...(1)

`32=ab^6` ...(2)

Divide equation (2) by equation (1).

`(32)/(8)=(ab^6)/(ab^4)`

`4=b^2`

Taking square root on both sides.

`2=b`

Put b=2 in (1).

`8=a(2)^4`

`8=16a`

`(8)/(16)=a`

`0.5=a`

Substitute a=0.5 and b=2 in the given general exponential equation.

`y=0.5(2)^x`

Therefore, the correct option is C.